Multiple factors have to be taken into account when mobile telecommunication network providers make decisions about radio transmitter placement. Generally, area coverage and the average signal level provided are of prime importance in these decisions. These criteria give rise to a bi-objective problem of facility location, with the goal of achieving an acceptable trade-off between maximising the total area coverage and maximising the average signal level provided to the demand region by a network of radio transmitters. This paper establishes a mathematical modelling framework, based on these two placement criteria, for evaluating the effectiveness of a given set of radio transmitter locations. In the framework, coverage is measured according to the degree of obstruction of the so-called ‘Fresnel zone’ that is formed between handset and base station, while signal strength is modelled taking radio wave propagation loss into account. This framework is used to formulate a novel bi-objective facility location model that may form the basis for decision support aimed at identifying high-quality transmitter location trade-off solutions for mobile telecommunication network providers. But it may also find application in various other contexts (such as radar, watchtower, or surveillance camera placement optimisation).